TY - JOUR

T1 - Low temperature behaviour of the random field Ising model

AU - Domb, C.

AU - Entin-Wohlman, O.

PY - 1984/1/11

Y1 - 1984/1/11

N2 - A relationship is established between the Ising model in a random positive and negative magnetic field on a lattice with p=12. At T=0 each percolation cluster gives rise to a first-order transition at a different value of the field. There is a significant difference in behaviour between lattices for which pc12which have an infinite cluster, and pc12which do not. By considering the Bethe lattice and allowing the coordination number to become large, the results of the mean field approximation are reproduced. The above considerations do not apply to a Gaussian distribution of fields, and the absence of a first-order transition can be understood in this case. Since large clusters overturn for small fields there are clear indications of metastable behaviour.

AB - A relationship is established between the Ising model in a random positive and negative magnetic field on a lattice with p=12. At T=0 each percolation cluster gives rise to a first-order transition at a different value of the field. There is a significant difference in behaviour between lattices for which pc12which have an infinite cluster, and pc12which do not. By considering the Bethe lattice and allowing the coordination number to become large, the results of the mean field approximation are reproduced. The above considerations do not apply to a Gaussian distribution of fields, and the absence of a first-order transition can be understood in this case. Since large clusters overturn for small fields there are clear indications of metastable behaviour.

UR - http://www.scopus.com/inward/record.url?scp=36149043446&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/17/1/001

DO - 10.1088/0305-4470/17/1/001

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AN - SCOPUS:36149043446

SN - 1751-8113

VL - 17

SP - L1-L6

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 1

ER -